Projected Multi-Agent Consensus Equilibrium for Ptychographic Image Reconstruction

Ptychography is a computational imaging technique using multiple, overlapping, coherently illuminated snapshots to achieve nanometer resolution by solving a nonlinear phase-field recovery problem. Ptychography is vital for imaging of manufactured nanomaterials, but existing algorithms have computational shortcomings that limit large-scale application. In this paper, we present the Projected Multi-Agent Consensus Equilibrium (PMACE) approach for solving the ptychography inversion problem. This approach extends earlier work on MACE, which formulates an inversion problem as an equilibrium among multiple agents, each acting independently to update a full reconstruction. In PMACE, each agent acts on a portion (projection) corresponding to one of the snapshots, and these updates to projections are then combined to give an update to the full reconstruction. The resulting algorithm is easily parallelized, with convergence properties inherited from convergence results associated with MACE. We apply our method on simulated data and demonstrate that it outperforms competing algorithms in both reconstruction quality and convergence speed.

[1]  øöö Blockinø Phase retrieval, error reduction algorithm, and Fienup variants: A view from convex optimization , 2002 .

[2]  D. R. Luke Relaxed averaged alternating reflections for diffraction imaging , 2004, math/0405208.

[3]  J. Rodenburg,et al.  A phase retrieval algorithm for shifting illumination , 2004 .

[4]  Charles A. Bouman,et al.  Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibrium , 2017, SIAM J. Imaging Sci..

[5]  Brendt Wohlberg,et al.  Plug-and-Play priors for model based reconstruction , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[6]  S. Marchesini,et al.  Alternating projection, ptychographic imaging and phase synchronization , 2014, 1402.0550.

[7]  Charles A. Bouman,et al.  Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation , 2015, IEEE Transactions on Computational Imaging.

[8]  Veit Elser Phase retrieval by iterated projections. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[9]  Talita Perciano,et al.  SHARP: a distributed, GPU-based ptychographic solver , 2016, 1602.01448.

[10]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[11]  Justin P. Haldar,et al.  Accelerated Wirtinger Flow: A fast algorithm for ptychography , 2018, 1806.05546.

[12]  P. Thibault X-ray ptychography , 2011 .

[13]  J. Rodenburg,et al.  An improved ptychographical phase retrieval algorithm for diffractive imaging. , 2009, Ultramicroscopy.